能级密度的半经典壳结构微-宏观方法
Semiclassical shell-structure micro-macroscopic approach for the level density
摘要：
在平均场半经典双轨道理论下，超越费米气体模型的鞍点方法，导出了具有给定能量$E$和粒子数$A$的单组分核子系统的能级密度$ρ(E,A)$.我们得到了$~~ρ\propto I_ν(S)/S^ν$，其中$I_ν(S)$是熵$S$的修正贝塞尔函数。在微观-宏观-正则近似（MMA）内，对于小的热激发能$U$，相对于旋转激发$E_{\rm rot}$，人们获得对于$ρ(E,A)$的$ν=3/2$。在激发能$U$大于$E_{\rm rot}$但小于中子分离能的情况下，发现$ν=5/2$的值较大。讨论了旋转核中固定自旋变量的作用。MMA能级密度$ρ$达到了与大激发能相关的大$S$的公知巨正则系综极限（费米气体渐近），并且还达到了低激发能（恒定“温度”模型）下小组合熵$S$的有限微正则极限。将MMA的$ρ(E,A)$与低激发能的实验数据拟合，考虑壳效应和定性的配对效应，得到的反能级密度参数$K$的值与从中子共振数据导出的参数基本不同。
英文摘要：
Level density $ρ(E,A)$ is derived for a one-component nucleon system with a given energy $E$ and particle number $A$ within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain $~~ρ\propto I_ν(S)/S^ν$, with $I_ν(S)$ being the modified Bessel function of the entropy $S$. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy, $U$, with respect to rotational excitations, $E_{\rm rot}$, one obtains $ν=3/2$ for $ρ(E,A)$. In the case of excitation energy $U$ larger than $E_{\rm rot}$ but smaller than the neutron separation energy, one finds a larger value of $ν=5/2$. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density $ρ$ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptotic) for large $S$ related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy $S$ at low excitation energies (the constant "temperature" model). Fitting the $ρ(E,A)$ of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter $K$ a value which differs essentially from that parameter derived from data on neutron resonances.
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